(328e) Dynamic Canonical Correlation Analysis for the Extraction and Diagnosis of Plant-Wide Oscillations

In this work, we present a newly developed dynamic data modeling algorithm, that is, DiCCA (dynamic-inner canonical component analysis) to extract a set of latent variables that have maximized auto-correlations. This DiCCA algorithm is different from prior versions of dynamic extensions of CCA as it derives explicit inner dynamic models with the objective to maximize the canonical correlations. As a consequence, the extracted dynamic components are most predictable from their past values.

Since oscillating signals are one of the most predictable types of signals, DiCCA is effective to extract oscillating latent variables among a set of process variables. The Tennessee Eastman oscillating dataset has been studied for root cause analysis. However, in most literature, only low frequency oscillations are examined. Higher frequency oscillations are either undiscovered or ignored. In fact, due to feedback and cascade controls, oscillations at different frequencies often interact with each other and result in a compounding effect. Therefore, a comprehensive analysis of oscillations at all frequencies is necessary for understanding the process and diagnosing the root cause.

In the Tennessee Eastman oscillating dataset, two different oscillations are discovered after DiCCA modeling. One is the well known low frequency oscillation with a period of 340 samples, the other one is a high frequency oscillation with a period of 18 samples. This high frequency oscillation has not been discovered previously.

Pairwise spectral granger causality analysis is performed on the variables with high frequency oscillations for the root cause analysis, and PC2.OP and PC2.PV are identified as the root cause. By applying the curve fitting method, it is further confirmed that valve stiction, rather than outside disturbance or aggressive tuning, causes the high frequency oscillations. The same analysis is conducted on the variables with low frequency oscillations as well, where LC2.OP and LC2.PV are identified as the root cause, and valve stiction is diagnosed as the physical reason. This corroborates with the conclusions in the paper of Thornhill et al. (2003), where LC2 control valve is confirmed as the root cause of the low frequency oscillations after an online test. This consistency demonstrates the effectiveness of DiCCA based analysis.

In addition, we analyze a set of data collected after LC2 valve was fixed. After DiCCA modeling, it is found that there is an oscillation with a period of 133 samples. Although the PC2 control valve was not fixed, the high frequency oscillations became less pronounced in this fixed dataset. One possible explanation for this observation is that oscillations at different frequencies interact with each other due to feedback and cascade controls. Therefore, fixing one control valve can change the other oscillation patterns.

In this work, DiCCA is demonstrated as an effective tool to analyze oscillating data. The newly discovered high frequency oscillations are studied and the root cause is identified. This analysis can be used as a standard way to study plant-wide oscillating datasets in the future.